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[Merged by Bors] - feat(CategoryTheory/Triangulated): more API #10527

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@joelriou joelriou commented Feb 14, 2024

In this PR, it is shown that in order to show that a pretriangulated category is triangulated category, i.e. in order to check the octahedron axiom, it is possible to replace a given diagram by an isomorphic diagram. This shall be used in #9550 in order to show that the homotopy category of cochain complexes in an additive category is triangulated.


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Thanks!
bors r+

@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot added ready-to-merge This PR has been sent to bors. and removed awaiting-review labels Feb 19, 2024
mathlib-bors bot pushed a commit that referenced this pull request Feb 19, 2024
In this PR, it is shown that in order to show that a pretriangulated category is triangulated category, i.e. in order to check the octahedron axiom, it is possible to replace a given diagram by an isomorphic diagram. This shall be used in #9550 in order to show that the homotopy category of cochain complexes in an additive category is triangulated.
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mathlib-bors bot commented Feb 19, 2024

Pull request successfully merged into master.

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@mathlib-bors mathlib-bors bot changed the title feat(CategoryTheory/Triangulated): more API [Merged by Bors] - feat(CategoryTheory/Triangulated): more API Feb 19, 2024
@mathlib-bors mathlib-bors bot closed this Feb 19, 2024
@mathlib-bors mathlib-bors bot deleted the triangulated-more-api branch February 19, 2024 21:11
thorimur pushed a commit that referenced this pull request Feb 24, 2024
In this PR, it is shown that in order to show that a pretriangulated category is triangulated category, i.e. in order to check the octahedron axiom, it is possible to replace a given diagram by an isomorphic diagram. This shall be used in #9550 in order to show that the homotopy category of cochain complexes in an additive category is triangulated.
thorimur pushed a commit that referenced this pull request Feb 26, 2024
In this PR, it is shown that in order to show that a pretriangulated category is triangulated category, i.e. in order to check the octahedron axiom, it is possible to replace a given diagram by an isomorphic diagram. This shall be used in #9550 in order to show that the homotopy category of cochain complexes in an additive category is triangulated.
riccardobrasca pushed a commit that referenced this pull request Mar 1, 2024
In this PR, it is shown that in order to show that a pretriangulated category is triangulated category, i.e. in order to check the octahedron axiom, it is possible to replace a given diagram by an isomorphic diagram. This shall be used in #9550 in order to show that the homotopy category of cochain complexes in an additive category is triangulated.
dagurtomas pushed a commit that referenced this pull request Mar 22, 2024
In this PR, it is shown that in order to show that a pretriangulated category is triangulated category, i.e. in order to check the octahedron axiom, it is possible to replace a given diagram by an isomorphic diagram. This shall be used in #9550 in order to show that the homotopy category of cochain complexes in an additive category is triangulated.
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3 participants